Calibration of a rotationally scanning position-tracking device

Abstract

This invention is a method for calibrating a two beam rotationally scanned light beam interruption coordinate data input device. In particular, four reference objects which can be sensed by the effectively rotating directional sensor are disposed at measured equal interval distances along an essentially straight line. The four reference objects are positioned relative to the effectively rotating directional sensor so that each of the objects can be essentially individually sensed in turn in the course of effective rotation of the sensor. The effective angular velocity and effective center of rotation of the sensor is then determined from the known distance between adjacent reference objects and the measured time intervals between detection of adjacent pairs of reference objects by the effectively rotating directional sensor. The effective angular velocity is first determined and then the effective center of rotation of the sensor is determined from the angular velocity, distance between reference objects, and measured time intervals.

We claim: 
     
       1. A calibration method for determining the effective position and effective angular velocity of an effectively rotating directional sensor comprising: (a) placing four reference objects which can be sensed by the effectively rotating directional sensor at measured substantially equal-interval distances along an essentially straight line, the four reference objects being positioned relative to the effectively rotating directional sensor so that each of the objects can be essentially individually sensed in turn in the course of effective rotation of the sensor;   (b) sensing each of the four reference objects in turn with the directional sensor during effective rotation of the sensor to determine three time intervals denoted μ 1 , μ 2 , μ 3 , one time interval being the time between the sensing of a corresponding one of the three adjacent pairs of reference objects;   (c) determining an effective rotational velocity α defined by a value of α for which the expression   sin α(μ.sub.1 +μ.sub.2) sin α(μ.sub.2 +μ.sub.3)-4 sin αμ.sub.1 sin αμ.sub.3        is essentially equal to zero; and   (d) trigonometrically determining the effective center of rotation of the sensor from the effective angular velocity, the measured time intervals, and the distance between adjacent reference objects.   
     
     
       2. A calibration method for a beam scanned coordinate-data input device having a rotating mirror for scanning, comprising: placing at least four reference objects along an essentially straight line which can be sensed by said beam scanned coordinate-data input device, a distance between any two adjacent reference objects being predetermined;   sensing each of said four reference objects with said scanned coordinate-data input device;   determining three time intervals, μ 1 , μ 2 , and μ 3 , each of said time intervals corresponding to the time between said sensing of adjacent reference objects;   determining an effective rotational velocity α of said rotating mirror in said scanned coordinate-data input device from said three time intervals;   trigonometrically determining the effective positional coordinates of a center of rotation for said rotating mirror with respect to said reference objects from α, said three time intervals, and said distances between said four reference objects.   
     
     
       3. A calibration method for a beam scanned coordinate-data input device having a rotating mirror for scanning, as in claim 2, wherein: said distance between a first pair of adjacent reference objects is approximately equal to a distance between a second pair of adjacent reference objects.   
     
     
       4. A calibration method for a beam scanned coordinate-data input device having a rotating mirror for scanning, as in claim 2, wherein: μ 1 , μ 2 , μ 3 , and α are related such that; (sin α(μ 1  +μ 2 )) (sin α(μ 2  +μ 3 )) is essentially equal to 4(sin(αμ 1 ) sin(αμ 3 )).   
     
     
       5. A calibration method for a beam scanned coordinate-data input device having a rotating mirror for scanning, as in claim 2, further comprising: determining the magnitude of the index angular difference between the position of the mechanical sweep movement when the electrical signal indicating the beginning of a mechanical scanning sweep movement occurs and a base line through the scanning axis, and   correcting by at least one of addition or subtraction said index angular difference from the indicated angle at each scanning light interruption event.   
     
     
       6. A calibration method for a beam scanned coordinate-data input device having a rotating mirror for scanning, as in claim 5, wherein: said distance between a first pair of adjacent reference objects is approximately equal to a distance between a second pair of adjacent reference objects.   
     
     
       7. A calibration method for a beam scanned coordinate-data input device having a rotating mirror for scanning, as in claim 6, wherein: μ 1 , μ 2 , μ 3 , and α are related such that, (sin α(μ 1  +μ 2 )) (sin α(μ 2  +μ 3 )) is essentially equal to 4(sin(αμ 1 ) sin(αμ 3 )).